There is no such thing, as "ventless." It is just venting in a different way.
In an existing fireplace (masonary/metal) it'll vent past a closed leaky damper. In Eastie's case, plumber suggest leaving damper slightly open. Hello, vented!
In loosely built homes, vented thru the cracks, windows,ceilings, existing duct, doors, etc. Hello, vented! You tighten up these areas, you could have moisture related issues. (health/home repair) It is well documented, in the hvac world.
An old school masonary/metal woodburning fireplace, burning oak, produces about 100,000 btuh of heat. The chimney, is designed for that much heat vented material/burnt fuel. A set of 20" gas logs, used in that same fireplace, produces about 40,000 buth of heat. With flue open, you will feel cold air, fall out the fireplace. You have to reduce the damper opening, to reduce the draftiness. (Most gas log sets, include a clamp thingie, to make this adjustment.)
NOTE: btuh difference. Efficiency is actually about the same. About 50% So oak, puts out twice the heat, but also needs about twice the fresh make-up air, to function. Not talking about enclosed gas fireplace/stove system, that's a different thing.
Been awhile, since I sold any gas hearth systems, or log sets.
My company policy, is we never recommend or install ventless gas logs.
Everything has a trade off.
Mastercraft 205, Chevy 5.7 TBI.